The operator of a pumping station has observed that demand for water during early afternoon hours has an approximately exponential distribution with mean 100 cfs (cubic feet per second). (a) Find the probability that the demand will exceed 250 cfs during the early afternoon on a randomly selected day. (Round your answer to four decimal places.) (b) What water-pumping capacity, in cubic feet per second, should the station maintain during early afternoons so that the probability that demand will exceed capacity on a randomly selected day is only 0.02? (Round your answer to two decimal places.) cfs

A maintenance person has the job of keeping two machines in working order. The amount of time that a machine works before breaking down has an exponential distribution with a mean of 10 hours. The time then spent by the maintenance person repairing the machine has an exponential distribution with a mean of 8 hours. A. Show that this process fits the birth-and-death process by defining the states, specifying the values of the λn and μn, and then constructing the rate diagram. (Hint: Let the state represent the number of machines that are broken down). B. Calculate the Pn. C. Calculate L, Lq, W, and Wq. D. Determine the proportion of time that the maintenance person is busy. E. Determine the proportion of time that any given machine is working.  Need the excel formula, if necessary

The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 7 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement. In a room of 1,000 people over age 81, how many do you expect will NOT have retired yet? (Round your answer to the nearest whole number.)

A safety engineer uses simple logistic regression tostudy the relationship between occupancy years (x)and evacuation decision (y), under a majorhurricane forecast. Each occupant willevacuate (Y = 1) or stay (Y = 0). Sample dataprovides the estimated logit function:w = 2.83 − 0.24x. Estimate the odds that ahomeowner of 10 years will evacuate.

The lifetime, in years, of a type of small electric motor operating under adverse conditions is exponentially distributed with λ = 3.500. Whenever a motor fails, it is replaced with another of the same type. Find the probability that fewer than six motors fail within one year. (Round the final answer to three decimal places.)

Suppose that the investigators want to control for whether a subject is over 60 years old in the logistic model from part (g) above. Let the variable Over60 = 1 if a subject is over 60 and 0 otherwise. They fit a logistic model with both Finasteride and Over60 as the predictors and obtain the following: Coefficients: Estimate (Intercept) -1.88067 Finasteride -0.34736 Over60 1.32285 Std. Error 0.05075 0.05355 0.05589 z value -37.059 -6.486 23.670 Pr(>|z|) < 2e-16 8.79e-11 < 2e-16 *** Estimated odds ratio associated with the coefficient for the Over60 predictor: *** *** What is the interpretation of the estimated odds ratio associated with the coefficient for the Over 60 predictor? The odds of developing cancer among those 60 years old and older are those aged under 60 years, adjusting for Finasteride treatment group, using a 5% significance level. times

For the 23 space shuttle flights before the Challenger mission disaster in 1986, The following table shows the temperature (◦F) at the time of the flight and whether at least one primary O-ring suffered thermal distress. Use logistic regression to model the effect of temperature on the probability of thermal distress. Interpret the effect. Estimate the probability of thermal distress at 31◦F, the temperature at the time of the Challenger flight. At what temperature does the estimated probability equal 0.50? At that temperature, give a linear approximation for the change in the estimated probability per degree increase in temperature. Interpret the effect of temperature on the odds of thermal distress. Test the hypothesis that temperature has no effect, using (i) the Wald test, (ii) the likelihood-ratio test.

An article in a magazine discussed the length of time till failure of a particular product. At the end of the product's lifetime, the time till failure is modeled using an exponential distribution with a mean of 500 thousand hours. In reliability jargon this is known as the "wear-out" distribution for the product. During its normal (useful) life, assume the product's time till failure is uniformly distributed over the range 200 thousand to 1 million hours. Complete parts a through c. a. At the end of the product's lifetime, find the probability that the product fails before 600 thousand hours. (Round to four decimal places as needed.)

Consider a cohort of patients receiving an experimental two-year treatment for a serious disease. Suppose that only 20% of the patients survive to the end of the second year. Assume CFM (constant force of mortality) within each year of treatment. Find the probability that a patient who survives the first four months dies by the end of the 20th month. Round to 4 decimal places.

I only need B,C, and D